Inspired by this, Tsabary et al. [1]} studied miners' strategies in choosing different starting up times by establishing a “gap game", in which the miner's utility is comprehensively modeled by considering the expected income and cost. Based on this, they concluded that such a gap forms well before fees are the only incentive. Considering that [1]} was carried out under the quasi-static state assumption, Di et al. [3]} analyzed a dynamic game with more realistic hypotheses. Consequently, they mentioned that the decentralization of blockchain is heavily threatened in this case. In addition, [4]} and [5]} illustrated the above game differently via adopting “consensus game" and stochastic game, respectively. This provides us another view of investigating the miners' strategic actions as well as the stability of blockchain. Moreover, Arenas et al. [5]} put forward that the undercutting strategy is a better option for the miners than the honest strategy, i.e., mining on the longest chain, under the transaction fee-incentive regime, which is consistent with the statement in [7]}. While Gong et al. in [8]} pointed out that contrary to the primary belief, the undercutting behavior is not always beneficial to miners, especially when other miners are aware of these kinds of actions.
